A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls
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A rigorous mathematical analysis is given for a boundary layer problem for a third-order nonlinear ordinary differential equation, which arises in gravity-driven laminar film flow of power-law fluids along vertical walls. Firstly, the problem is transformed into a singular nonlinear two-point boundary value problem of second order. Next, the latter is proved to have a unique positive solution, for which some estimates are established. Finally, the result above-mentioned is turned over to the original problem. The conclusion of this paper is that the boundary layer problem has a unique normal solution if the power-law index is less than or equal to one and a generalized normal solution if the power-law index is greater than one. Also the asymptotic behavior of the normal solution at the infinity is displayed.
Mathematics Subject Classification (2000).76A05 76D10 34B15
Keywords.Boundary layer problem power-law index (generalized) normal solution singular nonlinear two-point boundary value problem positive solution existence uniqueness
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